The coordinates of the vertices of jkl are j(-5, -1), k(0, 1) , and l(2, -5). which statement correctly describes whether jkl is a right triangle?

It is NOT a right triangle.

Step-by-step explanation:

You must figure out the slopes of the segments of the triangle to see if it is a right triangle. If they are perpendicular (meaning the slopes are negative reciprocals of each other), they form a right angle, making it a right triangle.

This formula finds slope using two points.

Let's figure out the slope of JK.

(-1-1)/(-5-0) = m

Simplify.

-2/-5 = m

A negative divided by a negative makes a positive.

2/5 = m

Now LK.

(-5-1)/(2-0) = m

Simplify.

-6/2 = m

Divide.

-3/1 = m

Now JL.

(-1+5)/(-5-2) = m

Simplify.

4/-3 = m

None of these slopes are negative reciprocals of each other, thus deeming it not a right triangle.

for the friend request.

when a figure, such as triangle (xyz) is reflected over the line y = x to create x'y'z' the x-coordinates and y-coordinates of the original image (pre-image) will be reversed for the image. (e.g., (x, y) > (y, x)) this means that the pre-image position of the x- and y-coordinates switch places which in turn provides a mirror like image of the original xyz.  

i notice that when i draw a line segment from x to x', that the points are parallel from each other -- they are exactly across from each other and do not intersect with any other points.  

yes, think i would see the same characteristic if you drew the line segment connecting y with the reflecting line and then y' with the reflecting line because of the essence of reflections. because it is a mirror image, each point was effected the same way which leads me to conclude that they same would apply to y and y'.